What is the difference between probabilistic forecasting and quantile forecasting?

A probabilistic time series forecast outputs the entire distribution of the forecasted values for a given time point, instead of just a mean or a point forecast.

A quantile forecast is a forecast where instead of the median or the mean we forecast at various quantiles of the forecast value.

Although the mathematical expressions are different for the two, aren't they essentially the same "in spirit", in the sense that generating a sufficiently granular quantile forecast gives us the same thing as a probabilistic forecast?